Make sure the northmarker is pointing in the right direction. Take the exterior building for angle calculation if the claim is a house, in case of dungeons you should take the door.

Make sure doors and windows are properly placed. Either doors and windows use the same meshes as the exterior building or the interior uses the appropriate equivalent.

In case of dungeons and basements, you have to ensure that the size and layout makes sense in relation to the surrounding exterior landscape.

If the exterior has chimneys, the interior must have a fireplace in the correct spot. If the exterior chimney has smoke, the fireplace should be lit.

Part 2: General stuff

File must not be dirty. Keep an eye out for custom objects that don't make files dirty as they have been added by the modder.

Custom objects must follow the respective project's naming scheme.

File must not be dependent on any .esm files other than the respective project's data files.

Make sure the interior has appropriate light settings.

A common house's ambient light settings should never go below a 40, 40, 40 grey unless it makes sense for it to be darker. Also, ambient light in houses should in general not exceed 71, 71, 71.

Dungeons should use darker settings; Again, values can vary, but ambient settings shouldn't go much higher than 60, 60, 60.

Fog density. Something higher than 1.15 is too high for houses, but fine for dungeons if it is applied for the sake of atmosphere; Everything below 1 is fine for houses but seems wrong in dungeons.

Check whether 'illegal to sleep here' is ticked. This should never be enabled in dungeons; in buildings, it is common for people not to be allowed to rest. There may be rare exceptions.

Blacksquares need to be placed by reviewers if the modder forgot to. Always check architecture sticking out of the shell!

Check the object list for ownership leftovers. Cookie cutting is not allowed.

No objects should exist outside of the interior shell unless they are blacksqr northmarkers.

Part 3: Placement issues

Check for all kinds of placement errors. Here's a list of common expressions you may use when listing them:

floating: An object is fully in mid-air, not touching the surface beneath it with any vertex.

bleeding: An object is partially stuck in another object, making them overlap in a way that is illogical and aesthetically unpleasing. Here's a small list of objects where bleeding is perfectly acceptable:

all kinds of sacks bleeding (a bit) into each other.

items with pointy bottoms sunk into the surface to hide this anomaly

tapestry holders bled into walls

chandelier holders bled into ceilings

thick rugs bled into the floor

pieces of furniture stuck together in a way that they form new, believable pieces

overlapping: A special form of a bleeder specific to architecture pieces like beams. They may be bled unless their x or y-coordinates are equal; in that case, they are overlapping and you have some sort of flickering effect that's harsh on the eyes.

caspering: You can see through the bottom of an object.

ghosting: The opposite of floating, kind of; an object is not connected to the ceiling it should hang from or the wall it should be attached to. Think of tapestries not touching walls or chandeliers that should naturally fall down because their chain isn't attached to the ceiling.

Part 4: Style-Mixing

While this seems trivial at first, it really is trickier than most people think. The fact we're working on Skyrim or Cyrodiil doesn't mean everything that is not Sky_ or PC_ is wrong; In fact, these points should be considered:

Do not desperately look for things that aren't the style you are primarily expecting to be in the interior. Some _com items like _com_lamps are perfectly fine in Redguard interiors, for example. Similarly, some _de items like de_cloth pieces or de_shack baskets are perfectly fine in all P:C interiors.

General rule of thumb: What looks wrong could be style-mixing, so check it out in detail.

Style-mixing doesn't only occur between com_, de_ and Nord_ items. There may be other cultures and furniture styles to consider, think of orc items or Reachmen decoration clutter in the ShotN project.

Mixing between _Nord_Low and _Nord_Upper or com_rm and com_r is also style-mixing. Keep in mind this may not always apply; in a rich man's palace, there may be a personal library using _Nord_Upper items and poor workers' quarters using _Nord_Low furniture, which is fine and even reasonable. Think first, then replace.

Make sure you have seen the concept/reference interior (if one exists) for a certain area before you review. We may allow certain objects in certain interiors.

Mixing poor-style furniture with ex_ furniture is allowed except if it looks particularly out of place.

Part 5: Context

It is required to adjust your 'reviewer senses' to all pieces of information given in the claim description and character designs. You shouldn't just download and start reviewing; make sure you have read up on all additional background knowledge in order to properly evaluate. Someone taking care of the local crypt may have barrow urns in their house even though it may seem weird in a commoner's place.

Part 6: The overall picture

This is very important: do not focus on placement errors like floaters, bleeders etc. only. As a reviewer, you need to look at things at detail as well as on a larger scale. Some things like style-mixing or weird things like objects leaning against loaddoors may be more immersion-breaking to most players than a tiny bleeder. Simply going through an interior and listing all kinds of bleeders and floaters shows dedication, but I would never consider it a proper, full review.

Part 6: More stuff

Additional things to consider (these are no less important than the other points; there's just less to say about them):

Teleports between cells: If the claim is divided into several sub-cells, make sure any associated cells are linked properly. Never rotate a marker on the x/y axes! Also make sure the player doesn't get teleported into objects/walls or some such.

Clutter. Things may be overcluttered or undercluttered regarding the situation and context. Clutter could be repetetive. Look for these kinds of things! Try to fix them without causing too much mayhem and without changing the original interior too much. Only make the changes necessary to prevent a boring/repetetive interior from passing review.

Style: Similar to clutter with a couple intersections between the two points. In general, make sure you don't count things as errors that are merely related to the individual style of a modder. However, if you would consider something 'bad style' in general, you may adjust it, but not to your own liking, but to an extend where it's not definitely considered 'bad style' from a player-point-of-view.
Also, if arrangement of objects/clutter does not fit the given context of the interior, it needs to be fixed with a minimum of adjustments made to the overall interior (until it's fine).

Expensive items: Be on the lookout for items that are too expensive to be in a place. This is, of course, related to the context of the interior; a common house with a big treasure isn't right, but the treasure would be fine in a deep dungeon or a noble's manor.

Unique items: Not sure if this needs further elaboration. Things like the Scroll of Icarian Flight have no place in any interior.

Lights: Keep in mind there shouldn't (generally) be too many lights in one spot. If too many light radii overlap, it looks bad ingame. To check the radius, press 'l' in the CS.

Locks: Make sure chests are appropriately locked! A chest containing jewelry that is easily accessed by anyone? Nah.

Pitchers without nopickup: This is important. If you put a flower in a vase, and the player picks up the vase, what about the flower? The vanilla game implemented the 'nopickup' script. Make sure it is applied to objects! If a modder applied it to an existing object without creating a new one, fix that! It will be dirty, but when you clean the file, naturally you should create this nopickup pitcher!

Objects with scripts on them: Some objects may be scripted to appear at certain times only or they are related to certain events, these could also belong into the 'unique items' category, but some are not quite that obvious.

Things needing rotation/variation: A lot of times people copy-paste misc items and just place them next to one another without adjusting scale, rotation, etc. This may not be a big issue, but it does break immersion. If it is too apparent you may fix it by any means possible.

Faction-specific items: Some items look fine, but are faction-specific. Think about the Fighter's Guild chests with equipment, for instance. Even experienced modders may accidentally place these kinds of containers! (In general, you should check content of containers to make sure what's in there actually makes sense in the given interior. An alchemist with a chest containing 5 or 6 weapons? I don't think so.)
Another example, specific Tribunal banners and/or tapestries. Of course, you shouldn't just be on the lookout for Tribunal banners now. Apply these hints to the overall mod and game and to all objects you can think of.

That last point is significant. Don't just look for my examples here. These are just, well, examples. I could give you more examples, but you should be able to detect these yourself after reading this and applying the information/rules.

Part 7: Cookies

Another common rule of thumb: Never remove items unless they don't belong. Also, don't change things that aren't wrong. A reviewer needs to be impartial!

Lastly, test the file in the actual game and check if all places are properly accessible. In houses, you should also test whether all doors open properly.

I may add more points as they come to my mind, so keep checking back. That's it.